Progress in Mathematics

Symplectic Geometry and Secondary Characteristic Classes

Authors: Vaisman, Izu

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About this book

The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in­ terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre­ viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome­ try and topology, and in the applications to physical theories.

Table of contents (4 chapters)

  • Introduction and Motivation

    Vaisman, Izu

    Pages 1-21

  • Symplectic Vector Spaces

    Vaisman, Izu

    Pages 23-52

  • Symplectic Geometry on Manifolds

    Vaisman, Izu

    Pages 53-101

  • Transversality Obstructions of Lagrangian Subbundles (Maslov Classes)

    Vaisman, Izu

    Pages 103-205

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4757-1960-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4757-1962-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Symplectic Geometry and Secondary Characteristic Classes
Authors
Series Title
Progress in Mathematics
Copyright
1987
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-1960-4
DOI
10.1007/978-1-4757-1960-4
Softcover ISBN
978-1-4757-1962-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
IX, 216
Topics